Bounding $ζ(s)$ in the critical strip

Details Bounding $ζ(s)$ in the critical strip Bounding $ζ(s)$ in the critical strip

2010-08-29

arxiv.org/abs/1008.4970v1

Journal of Number Theory (Print), v. 131, p. 363-384, 2011

Mathematics

Number Theory

Scientific paper

10.1016/j.jnt.2010.08.002

Assuming the Riemann Hypothesis, we make use of the recently discovered \cite{CLV} extremal majorants and minorants of prescribed exponential type for the function $\log\left(\tfrac{4 + x^2}{(\alpha-1/2)^2 + x^2}\right)$ to find upper and lower bounds with explicit constants for $\log|\zeta(\alpha + it)|$ in the critical strip, extending the work of Chandee and Soundararajan \cite{CS}.

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